Photodarkening in Yb doped fibers: experimental evidence of equilibrium states depending on the pump power

doi:10.1364/OE.15.014838

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Photodarkening in Yb doped fibers: experimental evidence of equilibrium states depending on the pump power

Sylvia Jetschke, Sonja Unger, Ulrich Röpke, and Johannes Kirchhof »View Author Affiliations

Optics Express, Vol. 15, Issue 22, pp. 14838-14843 (2007)
http://dx.doi.org/10.1364/OE.15.014838

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▸ Article Outline
– Abstract
1. Introduction
2. Fiber fabrication and standard characterization
3. Photodarkening measurements
4. Results and discussion
5. Conclusions
– References and links

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Abstract

Photodarkening in Yb doped fibers was examined at 633 nm in-situ during cladding pumping at 915 nm with varying pump powers and with no indication of an onset threshold. For the first time, the partial bleaching of the photodarkening loss by the pump power itself was observed. We found the relaxation to well-defined equilibrium states of the core excess loss, depending on the Yb inversion. From the dependence of the measured rate constant on the density of excited Yb ions we conclude, that on average 3 to 4 excited Yb ions create or bleach one color center responsible for the core excess loss.

1. Introduction

Photodarkening was observed in silica fibers doped with different rare earth ions [1–3

M. M. Broer, D. M. Krol, and D. J. DiGiovanni, “Highly nonlinear near-resonant photodarkening in a thulium-doped aluminosilicate glass fiber,” Opt. Lett. 18, 799–801 (1993). [CrossRef] [PubMed]

] and can seriously deteriorate the features of fiber lasers or amplifiers [4

I. Manek-Hönninger, J. Boullet, T. Cardinal, F. Guillen, M. Podgorski, R. Bello Doua, and F. Salin, “Photodarkening and photobleaching of an ytterbium-doped silica double-clad LMA fiber,” Opt. Express 15, 1606–1611 (2007). [CrossRef] [PubMed]

, 5

B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J.-P. Martin, and J.-P. De Sandro, “Low photodarkening single cladding ytterbium fibre amplifier,” in Fiber Lasers IV: Technology, Systems, and Applications, D. J. Harter, A. Tünnermann, J. Broeng, and C. Headley, eds., Proc. SPIE 6453, 64530H-1–9 (2007). [CrossRef]

]. It has been shown, that the phenomenon is initiated by a high Yb inversion [3

J. J. Koponen, M. J. Söderlund, H. J. Hoffmann, and S. K. T. Tammela, “Measuring photodarkening from single-mode ytterbium doped silica fibers,” Opt. Express 14, 11539–11544 (2006). [CrossRef] [PubMed]

, 4

] and not primarily by intense pump or laser power. The generation of color centers responsible for the measured loss in the UV/VIS/IR wavelength range was attributed to a photo-ionization process powered by the energy of excited Yb ions. Photodarkening in Yb doped fibers can also be induced by 488 nm irradiation [6

S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, “Photodarkening in Yb-doped aluminosilicate fibers induced by 488nm irradiation,” Opt. Lett. 32, 1626–1628 (2007). [CrossRef] [PubMed]

]. The bleaching of the photodarkening excess loss by UV irradiation [4

] and also by heat treatment > 200 °C [7

J. Jasapara, M. Andrejco, D. DiGiovanni, and R. Windeler, “Effect of heat and H₂ gas on the photodarkening of Yb³⁺ fibers,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies 2006, Technical Digest (Optical Society of America, Washington, DC, 2006), CTuQ5.

, 8

A. V. Shubin, M. V. Yashkov, M. A. Melkumov, S. A. Smirnow, I. A. Bufetov, and E. M. Dianov, “Photodarkening of aluminosilicate and phosphosilicate Yb-doped fibers,” in Conf. Digest of CLEO Europe-EQEC 2007, CJ3-1-THU.

] was reported.

Several measurement techniques to investigate the temporal and spectral characteristics of the loss evolution were developed [3–9

]. Cladding pumping is advantageous, because an homogeneous Yb inversion can be achieved, independent of the core diameter and adjustable in a wide range with moderate pump powers. However, some of the reported measurement results suffer from errors due to a part of probe light guided in the cladding of the Yb fiber without attenuation. Thereby, the determined photodarkening loss can be orders of magnitude lower than the real core excess loss. Moreover, a saturation of the photodarkening at a low loss level may be pretended by the remaining cladding power, although the core is further darkened. The measurement of real core excess loss up to 2000 dB/m with cladding pumping was reported in [8

], and should also be possible with the setup described in [9

J. Koponen, M. Söderlund, H. J. Hoffman, D. Kliner, and J. Koplow, “Photodarkening Measurements in Large-Mode-Area Fibers,” in Fiber Lasers IV: Technology, Systems, and Applications, D. J. Harter, A. Tünnermann, J. Broeng, and C. Headley, eds., Proc. SPIE 6453, 64531E-1–11 (2007). [CrossRef]

The precise evaluation of the real core excess loss is essential to get a deeper insight in the photodarkening mechanism and to compare the properties of different fibers. In our work, the photodarkening is examined in-situ during cladding pumping with 915 nm. The measuring method is aimed at the determination of the real core excess loss without falsification by additional probe power guided in the cladding of the Yb fiber under test.

To describe the photodarkening process empirically, a stretched exponential function was used to fit the temporal decrease of the fiber transmission [6

, 9

]. However, the parameters determined in this way still depend on the fiber length. Real material parameters are obtained by modeling the time dependence of the core excess loss with a stretched exponential function, as it was suggested in [8

]. We use this model in an expanded form to analyze our measurement results and to understand photodarkening in Yb doped fibers as a relaxation process to an equilibrium state of generation and annihilation of color centers by excited Yb ions.

2. Fiber fabrication and standard characterization

Preform and fiber samples have been prepared by MCVD (Modified Chemical Vapor Deposition) and solution doping according to a route with carefully controlled process steps described in [10

J. Kirchhof, S. Unger, A. Schwuchow, S. Grimm, and V. Reichel, “Materials for high-power fiber lasers,” J. Non-Cryst. Solids 352, 2399–2403 (2006). [CrossRef]

, 11

J. Kirchhof, S. Unger, and A. Schwuchow, “Properties of Yb-doped materials for solid and microstructured high power fiber lasers,” in Proceedings of ICMAT 2007 Symposium on Microstructured and Nanostructured Optical Fibers, Singapore, 1–6 July, 2007.

]. The goal of the series prepared here was to provide nearly similar fibers codoped with constant amounts of 0.5 mol% P₂O₅ and 4 mol% Al₂O₃ and collapsed in oxygen atmosphere (compare [10

J. Kirchhof, S. Unger, A. Schwuchow, S. Grimm, and V. Reichel, “Materials for high-power fiber lasers,” J. Non-Cryst. Solids 352, 2399–2403 (2006). [CrossRef]

]), which primarily differ in their ytterbium content.

The samples were characterized by refractive index profiling, X-ray microprobe analysis and absorption and fluorescence measurements in VIS and NIR. Important properties are shown in Table 1. All fibers investigated have core and cladding diameters of 10 and 125μm, respectively.

Noteworthy with regard to the investigations described here is the observation, that for higher concentrations above 0.6 mol% Yb₂O₃ (N = 2.65 10²⁶ m^-3) the fluorescence behavior of the samples is seriously changed. This is shown not only by the decrease of the measured fluorescence lifetime at 1020 nm, but also by a remarkable reduction of the fluorescence intensities both at 1020 and 500 nm (“cooperative fluorescence”), which are proportional to the ytterbium content at low concentrations [11

]. The effect of lifetime quenching was also described in [12

R. Paschotta, J. Nilsson, P. R. Barber, J. E. Caplen, A. C. Tropper, and D. C. Hanna, “Lifetime quenching in Yb-doped fibers,” Opt. Commun. 136, 375–378 (1997). [CrossRef]

Table 1. Fiber sample number, density of ytterbium ions N, core NA, Yb³⁺ near infrared fluorescence lifetime τ, and fiber background loss α at 1200 and 633 nm, respectively.

fiber sample	N / 10²⁶ m^-3	NA	τ / μs	α/ dB/km
				1200 nm	633 nm
#1	0.88	0.16	830	10	90
#2	2.00	0.19	840	11	400
#3	2.60	0.19	830	22	460
#4	3.54	0.20	790	32	970
#5	4.86	0.21	670	44	1600

3. Photodarkening measurements

The set-up for the measurement of the fiber transmission in-situ during cladding pumping at 915 nm is shown in Fig. 1(a). Modulated light from a halogen lamp with monochromator (633nm, spectral width about 25 nm) is used as a probe. The pump and probe power are free-space coupled with lenses and a dichroitic mirror DM1 (high transmission (HT) at 915 nm, high reflection (HR) at 633 nm) into a multimode fiber MMF with a diameter of 125 μm, NA 0.37. The Yb fiber under test is spliced between this multimode fiber and a single-clad fiber (SCF, similar to the common SMF28). Most of the probe and pump power (> 95% of the launched power) transmitted in the cladding is stripped by index matching gel between alumina plates (7 cm of uncoated fiber); the residual cladding light is completely removed in the following fiber length > 2 m by the high index acrylate coating.

Fig 1. (a) Experimental setup for the measurement of photodarkening; (b) Probe transmission measured at fiber #4 (L = 5 cm) in-situ during cladding pumping with different initial pump powers: 1 W (lilac), 1.8 W (cyan), 2.1 W (green), 3.7 W (red) and 6.1 W (blue); after application of the initial pump power for a sufficient time, the Yb fiber core was “fully darkened” by a pump power of 13.2 W (steep decrease of the transmission).

Another dichroitic mirror DM2 (HT 915 nm, HR 633 nm) eliminates > 99% of the residual pump power and arising ASE out of the core of the Yb fiber. The power level and the spectrum of the ASE can be measured directly behind this mirror with a power meter and an optical spectrum analyzer, respectively. The reflected probe signal (about 150 pW before photodarkening of the Yb fiber) is detected by a low-noise receiver and a lock-in amplifier (resulting noise equivalent power NEP = 0.1 pW). The infrared and green emission out of the Yb fiber core are further attenuated by filters to avoid the receiver overload; the remaining CW power is monitored by a digital volt meter (DVM).

The Yb doped fibers (Table 1) with core and cladding diameter of 10 and 125μm, respectively, were tested without any coating and immersed in pure water to lower the pump loss by scattering at surface contaminations, that were otherwise observed, when the fiber was held in air.

To avoid lasing or strong ASE in the Yb doped core, the feedback is suppressed by the multimode fiber at one side and an angle-polished connector at the output end of the SCF. The part of probe power, guided in the Yb fiber cladding without attenuation and captured into the core of the SCF, is kept very low by the matched core diameters and NA of both fibers and by a high splice quality.

The time-dependent transmission T(t) = P(t)/P₀ (P₀ and P(t) are the transmitted probe powers before and during darkening, respectively) was examined during cladding pumping of the Yb fibers #1 to #5 (Table 1) with different pump powers. In the first experiments, fiber lengths between 5 to 10 cm were used; typical results are shown in Fig. 1(b) with fiber #4 as an example. After a nearly constant transmission had been reached with the selected pump power, the highest available pump power (13.2 W) was applied for strong darkening of the fiber core and to estimate an upper limit of the part of undamped probe power captured from the cladding; a transmission of 0.003 … 0.02 was found for all fibers investigated. Hence one can conclude, that the real core excess loss can be underestimated in our measurements, but the error is < 10%, if the fiber transmission is kept above a value of 0.1.

4. Results and discussion

In the following experiments, fiber lengths of 1 to 2 cm were examined (depending on the Yb content) to permit the measurement of core losses of more than 500 dB/m with the transmission kept above 0.1. The time-dependent core excess loss was calculated with α(t) = - log(T(t))/L in units of dB/m (L is the fiber length).

Fig. 2. Core excess loss of fiber #3 (length L=1cm) for stepwise variation of the pump power; (a): darkening (red) with 1.0, 2.1, 3.7, 6.1, 10, 13.2 W, (b): bleaching (green) with 10, 6.1, 3.7, 2.1, 1.0, 0.6 W (the last reduction of the pump power was applied at 431 min); the stretched exponential functions determined by the fitting procedure are also shown as thin dashed black lines.

In Fig. 2(a), the temporal evolution of the photodarkening loss in fiber #3 for the stepwise enhancement of the pump power is shown. The application time of each power level was chosen to get a nearly steady state of the fiber transmission; the effect of suddenly enhanced pump power results in a steeper increase of loss. After using the highest available value, the pump power was reduced also stepwise, resulting in a reduction of the measured core excess loss (Fig. 2(b)). The cycle of darkening and bleaching can be repeated with very similar course of loss development. After switching off the pump power at any arbitrary time, the state is “frozen” at the achieved loss level. No remarkable change of the fiber transmission was observed during an observation period of up to three days.

The relaxation to equilibrium in each period with a constant pump power was modeled on the basis of a stretched exponential function, assuming an ensemble of intrinsic locally varying relaxation times [13

C. P. Lindsey and G. D. Patterson, “Detailed comparison of the Williams-Watts and Cole-Davidson functions,” J. Chem. Phys. 73, 3348–3357 (1980). [CrossRef]

]. The time-dependent core excess loss α(t) starts at t ₀ with α ₀ and develops according to

α (t) = (α_{0} - α_{eq}) \exp [- {(\frac{(t - t_{0})}{τ})}^{β}] + α_{eq} .

(1)

The approach to the equilibrium state is characterized by three intrinsic parameters: the core excess loss at equilibrium α _eq, the rate constant τ^-1, and the stretching parameter β. They are obtained from the measurement results by a least square fit. The fit curves are included in Fig. 2 and 3 as thin dashed black lines; the accordance with the measurement is excellent in most cases. The reproducibility of the determined rate constants is about ±20% for the fibers #2 to #5, but ±50% for fiber #1 because of the required long measurement time. The accuracy of the core excess loss values is determined by the error of the fiber length L (±5% for L=1cm) and a possible underestimation error of losses discussed above.

A typical example of photodarkening and photobleaching, respectively, for a selected pump power (3.7 W, fiber #3) is shown in Fig. 3. It demonstrates the existence of an equilibrium state α _eq, that will be aspired from a lower as well as from a higher darkening level. This holds for any original state of darkening α ₀, as was confirmed in further experiments.

Fig. 3. Photodarkening (red) and photobleaching (green, after darkening with a higher pump power) of fiber #3 with the same pump power of 3.7 W (sections of Fig. 2a and 2b with shifted time scale); the stretched exponential functions determined by the fitting procedure are shown as thin dashed black lines; in both cases the core excess loss converges to the equilibrium value α _eq ≈ 530 dB/m for t → ∞ (dotted line).

Fig. 4. Rate constant τ^-1 in a log-log plot (a) and equilibrium core excess loss α _eq in a linear plot (b) as a function of the Yb inversion, determined for stepwise photodarkening (full red circles) and photobleaching (green crosses) of fiber #3 (measurements and fitting curves see Fig. 2); the values determined for “fresh” fibers (α ₀ = 0) in a one-step darkening process are also included (open red squares). The dashed lines in (a) are linear fits.

The Yb inversion achieved by cladding pumping of a short fiber piece (pump depletion < 5%, negligible ASE) can be calculated from the launched pump power, the pump saturation power and the cross sections for Yb absorption and emission at the pump wavelength with an accuracy of about ±5% (results as in [9

]).

In Fig. 4, both the measured rate constant τ^-1 (a) and the equilibrium excess loss α _eq (b) are shown as functions of the Yb inversion for fiber #3, using a stepwise variation of pump power (Fig. 2). Very similar results were obtained also for “fresh” fibers (α ₀ = 0) with instant application of the corresponding pump power, proving the existence of real equilibrium states.

The dependency of the rate constant on the density of excited Yb ions [Yb^*] (product of the inversion and the density of Yb ions) is summarized in Fig. 5(a) for all fibers investigated. The slope of 3 to 3.5 in this log-log plot (also in Fig. 4(a)) can be interpreted as the mean number of excited Yb ions necessary for the generation or annihilation of one color center.

The equilibrium value of the core excess loss α _eq is linearly depending on [Yb^*], as Fig. 5(b) shows. From these results we may conclude, that photodarkening starts with the “first” excited Yb ions - there is no indication of a minimal necessary Yb content or inversion, that was assumed elsewhere [5

]. The slope of α _eq related to [Yb^*] seems to grow with the Yb content. The irregular behavior of the fibers #4 and #5 should be discussed in connection with the reduction of the Yb fluorescence lifetime and -intensity for high Yb content [11

For the stretching parameter β values between 0.4 and 0.7 were found. Even if its meaning is not quite clear yet, it relates the photodarkening process to many other relaxation phenomena in amorphous materials with very similar relaxation behavior [13

C. P. Lindsey and G. D. Patterson, “Detailed comparison of the Williams-Watts and Cole-Davidson functions,” J. Chem. Phys. 73, 3348–3357 (1980). [CrossRef]

Fig. 5. Rate constant τ^-1 in a log-log plot (a) and equilibrium core excess loss α _eq in a linear plot (b) in dependence on the density of excited Yb ions [Yb^*] for the fibers investigated (see Table 1): #1 (blue), #2 (cyan), #3 (olive), #4 (orange), and #5 (magenta). The solid lines are linear fits to the measured data.

5. Conclusions

For the first time, the partial bleaching of photodarkening in Yb doped fibers powered by the excited Yb ions has been observed. From the existence of well-defined photodarkening equilibrium states we conclude, that a limited Yb inversion level will not result in an unlimited increase of the photodarkening loss in the fiber types investigated. However, the expected equilibrium state for low Yb content and/or low inversion may be reached only after a very long operation time.

Since the measured rate constant depends on the density of excited Yb ions by a power law with an exponent close to 3.5, the energy of on average 3 to 4 excited Yb ions should be necessary for the process of generation or annihilation of one additional color center causing the photodarkening loss.

References and links

1.	M. M. Broer, D. M. Krol, and D. J. DiGiovanni, “Highly nonlinear near-resonant photodarkening in a thulium-doped aluminosilicate glass fiber,” Opt. Lett. 18, 799–801 (1993). [CrossRef] [PubMed]
2.	G. R. Atkins and A. L. G. Carter, “Photodarkening in Tb³⁺-doped phosphosilicate and germanosilicate optical fibers,” Opt. Lett. 19, 874–876 (1994). [CrossRef] [PubMed]
3.	J. J. Koponen, M. J. Söderlund, H. J. Hoffmann, and S. K. T. Tammela, “Measuring photodarkening from single-mode ytterbium doped silica fibers,” Opt. Express 14, 11539–11544 (2006). [CrossRef] [PubMed]
4.	I. Manek-Hönninger, J. Boullet, T. Cardinal, F. Guillen, M. Podgorski, R. Bello Doua, and F. Salin, “Photodarkening and photobleaching of an ytterbium-doped silica double-clad LMA fiber,” Opt. Express 15, 1606–1611 (2007). [CrossRef] [PubMed]
5.	B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J.-P. Martin, and J.-P. De Sandro, “Low photodarkening single cladding ytterbium fibre amplifier,” in Fiber Lasers IV: Technology, Systems, and Applications, D. J. Harter, A. Tünnermann, J. Broeng, and C. Headley, eds., Proc. SPIE 6453, 64530H-1–9 (2007). [CrossRef]
6.	S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, “Photodarkening in Yb-doped aluminosilicate fibers induced by 488nm irradiation,” Opt. Lett. 32, 1626–1628 (2007). [CrossRef] [PubMed]
7.	J. Jasapara, M. Andrejco, D. DiGiovanni, and R. Windeler, “Effect of heat and H₂ gas on the photodarkening of Yb³⁺ fibers,” in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies 2006, Technical Digest (Optical Society of America, Washington, DC, 2006), CTuQ5.
8.	A. V. Shubin, M. V. Yashkov, M. A. Melkumov, S. A. Smirnow, I. A. Bufetov, and E. M. Dianov, “Photodarkening of aluminosilicate and phosphosilicate Yb-doped fibers,” in Conf. Digest of CLEO Europe-EQEC 2007, CJ3-1-THU.
9.	J. Koponen, M. Söderlund, H. J. Hoffman, D. Kliner, and J. Koplow, “Photodarkening Measurements in Large-Mode-Area Fibers,” in Fiber Lasers IV: Technology, Systems, and Applications, D. J. Harter, A. Tünnermann, J. Broeng, and C. Headley, eds., Proc. SPIE 6453, 64531E-1–11 (2007). [CrossRef]
10.	J. Kirchhof, S. Unger, A. Schwuchow, S. Grimm, and V. Reichel, “Materials for high-power fiber lasers,” J. Non-Cryst. Solids 352, 2399–2403 (2006). [CrossRef]
11.	J. Kirchhof, S. Unger, and A. Schwuchow, “Properties of Yb-doped materials for solid and microstructured high power fiber lasers,” in Proceedings of ICMAT 2007 Symposium on Microstructured and Nanostructured Optical Fibers, Singapore, 1–6 July, 2007.
12.	R. Paschotta, J. Nilsson, P. R. Barber, J. E. Caplen, A. C. Tropper, and D. C. Hanna, “Lifetime quenching in Yb-doped fibers,” Opt. Commun. 136, 375–378 (1997). [CrossRef]
13.	C. P. Lindsey and G. D. Patterson, “Detailed comparison of the Williams-Watts and Cole-Davidson functions,” J. Chem. Phys. 73, 3348–3357 (1980). [CrossRef]

OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(160.2290) Materials : Fiber materials
(160.5690) Materials : Rare-earth-doped materials

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: August 27, 2007
Revised Manuscript: October 24, 2007
Manuscript Accepted: October 24, 2007
Published: October 25, 2007

Citation
Sylvia Jetschke, Sonja Unger, Ulrich Röpke, and Johannes Kirchhof, "Photodarkening in Yb doped fibers: experimental evidence of equilibrium states depending on the pump power," Opt. Express 15, 14838-14843 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-22-14838

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References

M. M. Broer, D. M. Krol, and D. J. DiGiovanni, "Highly nonlinear near-resonant photodarkening in a thulium-doped aluminosilicate glass fiber," Opt. Lett. 18, 799-801 (1993). [CrossRef] [PubMed]
G. R. Atkins and A. L. G. Carter, "Photodarkening in Tb3+-doped phosphosilicate and germanosilicate optical fibers," Opt. Lett. 19, 874-876 (1994). [CrossRef] [PubMed]
J. J. Koponen, M. J. Söderlund, H. J. Hoffmann, and S. K. T. Tammela, "Measuring photodarkening from single-mode ytterbium doped silica fibers," Opt. Express 14,11539-11544 (2006). [CrossRef] [PubMed]
I. Manek-Hönninger, J. Boullet, T. Cardinal, F. Guillen, M. Podgorski, R. Bello Doua, and F. Salin, "Photodarkening and photobleaching of an ytterbium-doped silica double-clad LMA fiber," Opt. Express 15, 1606-1611 (2007). [CrossRef] [PubMed]
B. Morasse, S. Chatigny, E. Gagnon, C. Hovington, J.-P. Martin, and J.-P. De Sandro, "Low photodarkening single cladding ytterbium fibre amplifier," in Fiber Lasers IV: Technology, Systems, and Applications, D. J. Harter, A. Tünnermann, J. Broeng, and C. Headley, eds., Proc. SPIE 6453, 64530H-1-9 (2007). [CrossRef]
S. Yoo, C. Basu, A. J. Boyland, C. Sones, J. Nilsson, J. K. Sahu, and D. Payne, "Photodarkening in Yb-doped aluminosilicate fibers induced by 488nm irradiation," Opt. Lett. 32, 1626-1628 (2007). [CrossRef] [PubMed]
J. Jasapara, M. Andrejco, D. DiGiovanni, and R. Windeler, "Effect of heat and H2 gas on the photodarkening of Yb3+ fibers," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies 2006, Technical Digest (Optical Society of America, Washington, DC, 2006), CTuQ5.
A. V. Shubin, M. V. Yashkov, M. A. Melkumov, S. A. Smirnow, I. A. Bufetov, and E. M. Dianov, "Photodarkening of aluminosilicate and phosphosilicate Yb-doped fibers," in Conf. Digest of CLEO Europe-EQEC 2007, CJ3-1-THU.
J. Koponen, M. Söderlund, H. J. Hoffman, D. Kliner, and J. Koplow, "Photodarkening Measurements in Large-Mode-Area Fibers," in Fiber Lasers IV: Technology, Systems, and Applications, D. J. Harter,A. Tünnermann, J. Broeng, and C. Headley, eds., Proc. SPIE 6453, 64531E-1-11 (2007). [CrossRef]
J. Kirchhof, S. Unger, A. Schwuchow, S. Grimm, and V. Reichel, "Materials for high-power fiber lasers," J. Non-Cryst. Solids 352, 2399-2403 (2006). [CrossRef]
J. Kirchhof, S. Unger, and A. Schwuchow, "Properties of Yb-doped materials for solid and microstructured high power fiber lasers," in Proceedings of ICMAT 2007 Symposium on Microstructured and Nanostructured Optical Fibers, Singapore, 1-6 July, 2007.
R. Paschotta, J. Nilsson, P. R. Barber, J. E. Caplen, A. C. Tropper, and D. C. Hanna, "Lifetime quenching in Yb-doped fibers," Opt. Commun. 136, 375-378 (1997). [CrossRef]
C. P. Lindsey and G. D. Patterson, "Detailed comparison of the Williams-Watts and Cole-Davidson functions," J. Chem. Phys. 73, 3348-3357 (1980). [CrossRef]

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